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math.rs
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math.rs
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use crate::structure::matrix::Matrix;
/// Mathematical Vector
///
/// # Description
/// Vector has two operations : addition, scalar multiplication.
/// And a space of the vector should closed for that operations.
pub trait Vector {
type Scalar;
fn add_vec(&self, rhs: &Self) -> Self;
fn sub_vec(&self, rhs: &Self) -> Self;
fn mul_scalar(&self, rhs: Self::Scalar) -> Self;
}
/// Kinds of Vector & Matrix norm
///
/// # Kinds of Vector norm
/// * `l1`
/// * `l2`
/// * `lp`
/// * `lInf`
///
/// # Kinds of Matrix norm
/// * `F`: Frobenius norm
/// * `lpq`: Element-wise pq norm
#[derive(Debug, Copy, Clone)]
pub enum Norm {
L1,
L2,
Lp(f64),
LInf,
F,
Lpq(f64, f64),
}
/// Normed Vector
pub trait Normed: Vector {
type UnsignedScalar;
fn norm(&self, kind: Norm) -> Self::UnsignedScalar;
fn normalize(&self, kind: Norm) -> Self
where
Self: Sized;
}
/// Inner product Vector
pub trait InnerProduct: Normed {
fn dot(&self, rhs: &Self) -> Self::Scalar;
}
/// Linear operation for Vector
pub trait LinearOp<T: Vector, S: Vector> {
fn apply(&self, rhs: &T) -> S;
}
/// Vector Products
pub trait VectorProduct: Vector {
fn cross(&self, other: &Self) -> Self;
fn outer(&self, other: &Self) -> Matrix;
}
/// Matrix Products
pub trait MatrixProduct {
fn kronecker(&self, other: &Self) -> Matrix;
fn hadamard(&self, other: &Self) -> Matrix;
}
// =============================================================================
// Implementation for primitive types
// =============================================================================
impl Vector for f64 {
type Scalar = Self;
fn add_vec(&self, rhs: &Self) -> Self {
self + rhs
}
fn sub_vec(&self, rhs: &Self) -> Self {
self - rhs
}
fn mul_scalar(&self, rhs: Self::Scalar) -> Self {
self * rhs
}
}
impl Normed for f64 {
type UnsignedScalar = f64;
fn norm(&self, _kind: Norm) -> Self::Scalar {
self.abs()
}
fn normalize(&self, _kind: Norm) -> Self
where
Self: Sized,
{
self / self.abs()
}
}